C. Judge - Systoles in translation surfaces

Christopher Judge (1) , Yohan Girard (2)

1 University of Maryland [College Park]
2 IF - Institut Fourier

I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of systoles (up to homotopy) in the strata H(2g-2) and the stratum H(1,1). We also determine the maximum systolic ratio (length squared/area) in H(2g-2), and we give a conjectural value for maximum systolic ratio in H(1,1).

Mots clés: Teichmüller dynamics mapping class groups and applications; Systoles; translation surfaces

Mots clés: eem2018; Grenoble

Domaines: Mathématiques [math]

Christopher Judge, Yohan Girard. C. Judge - Systoles in translation surfaces: Summer School 2018 - Teichmüller dynamics, mapping class groups and applications. 2018. ⟨medihal-01836343⟩